For the inductor, you know that the impedance is (jωL), and in this case, ωL = (5 ⨉ 103 rad/s )(0.2 ⨉ 10-3 H) = 1 Ω.

We're assuming a magnitude Vm for the (phasor) voltage, and taking its phase to be zero. Therefore, since the (phasor) current is given by the (phasor) voltage divided by the impedance:

IL = (Vm∠0) /(jωL) = (Vm) / (j) ​

Now, dividing by j is the same as multiplying by -j. Multplying by -j is the same as introducing a phase shift of -90°. To see this explicitly, you can write j in complex exponential form (if you are familiar with it):

-j = e-j(π/2)​

The phase angles of the other currents are determined in a similar way, by noting that current = voltage / impedance, and taking careful account of the phases of these two quantities.